Calibrating the Distance Scale

A period-luminosity relation allows us to read off a distance to a Cepheid variable once the scale is calibrated by finding the distance to any one Cepheid variable by other means. There were no Cepheid variables near enough to use standard parallax so the original distance scale was calibrated using the statistical parallax method. More recently, space-based observations have allowed true parallax to be used to calibrate the relation more precisely.

Cepheid Variables (2) ...

As first demonstrated by Henrietta Leavitt (see the right panel), there is a remarkable relationship between the period of pulsation and the luminosity (or absolute magnitude) for Cepheid variables. This permits Cepheid variables, in conjunction with the inverse square intensity law, to be used to determine distances. Such a relationship for a variable star is called a period-luminosity relation.
Period-Luminosity Relations
The figure shown below illustrates the light curve for delta Cephei and the period-luminosity relations for the two kinds of Cepheid variables. Given the period-luminosity relation (once it is calibrated; see the adjacent box) and knowing the type and period of the Cepheid, we can read the luminosity directly from the diagram. For example, a Pop II Cepheid with a period of 1 day has an absolute magnitude around -0.3 (which corresponds to a luminosity about 100 times that of the Sun). Once we know that, it is a simple matter to use the inverse square intensity law and the apparent magnitude to determine the distance to the star. Here is a Java applet that you can use to determine the distance to a Cepheid variable from its period and apparent magnitude.

Cepheids in Distant Galaxies
The adjacent image shows the spiral galaxy NGC 4414, as imaged by the Hubble Space Telescope. Although they can't be seen on the scale of this image, under high magnification individual Cepheid variables have been isolated in this galaxy. By making careful brightness measurements on these Cepheids, it was possible to determine that NGC 4414 lies at a distance of 19.1 megaparsecs (about 62 million light years).